Fork and storage

[Inmydomain]

 I have read a lot about storing in bitcoin in cold storage in case of a fork

What would be the impact of keeping bitcoin in exchange accounts e.g. coinbase?

[BitcoinHodler]

when a fork happens, all the coins that existed on old chain (all the unconfirmed transaction outputs) will exist on the new forked chain.

IF fork happens smoothly like the previous hard fork or other soft forks, then you won't even feel a thing. everything is going to continue as before.

IF the fork leads to a chain split. and two or more chains exist at the same time, all the coins that existed on the original chain will exist on the new chains too.
in this case if you have control over the private keys of those coins it means you can spend them on both chains. but if you don't have access to the private keys, you have no control over anything. your future is in the hands of the one controlling them for you in this case the exchanges or the coinbase wallet.

[Inmydomain]

And what would be the best option for generating and storing private keys?

[Barcode_]

I have read a lot about storing in bitcoin in cold storage in case of a fork

What would be the impact of keeping bitcoin in exchange accounts e.g. coinbase?

It would be better to store your bitcoins in cold wallet where you are fully in control of the private keys, if a fork really happens and the chain splits into two, you would still be able to spend your bitcoins on both chains. If you trust Coinbase that holds your bitcoins to handle this upcoming fork properly, you could still go ahead and store your bitcoins in their wallet, but I won't take the risk on that.